Unit 1 Basics of Geometry

Midpoint Property

If (x1, y1) and (x2, y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are: (X plus X divided by 2, and, Y plus Y divided by 2) Labeled as a coordinate pair (X, Y).

Undefined terms of Geometry

point, line, plane

Collinear Points

points that lie on the same line

Coplanar Points

points that lie on the same plane

Line Segment

consists of two points called the endpoints and all the points in between them that are collinear with the two points

Congruent segments

segments that have the same measure or length

Midpoint of a segment

the point on the segment that is same distance from both endpoints, midpoint bisects the segment

Ray

Portion of a line that contains all the points on the line that are on the same side of the first letter as the second letter

Angle

Two noncollinear rays having a common endpoint.

Adjacent Angles

two angles that share a common vertex and side, but have no common interior points

Measure of an angle

the smallest amount of rotation about the vertex from one ray to the other.

Protractor

a geometry tool used to measure angles

Congruent Angles

two angles that have the same measure

Angle Bisector

a ray that contains the vertex and divides the angle into two congruent angles

Counterexample

an example that proves that a statement is false

Parallel Lines

lines in the same plane that never intersect

Perpendicular Lines

lines that intersect at right angles (90 degrees)

Skew Lines

lines that are not in the same plane and do not intersect

Acute Angle

an angle that measures greater than 0 degrees and less than 90 degrees

Right Angle

an angle that measures 90 degrees

Obtuse Angle

An angle that measures more than 90 degrees but less than 180 degrees

Straight Angle

an angle that measures 180 degrees

Linear Pair

two adjacent angles whose noncommon sides are opposite rays

Vertical Angles

angles formed by 2 intersecting lines; they share a common vertex not a side

Complementary Angles

two angles whose measures have a sum of 90 degrees

supplementary angles

two angles whose measures have a sum of 180 degrees

Polygon

a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others

Three Sided Polygon

Triangle

Four Sided Polygon

quadrilateral

Five Sided Polygon

pentagon

Six Sided Polygon

hexagon

Seven Sided Polygon

heptagon

Eight Sided Polygon

octagon

Nine Sided Polygon

nonagon

Ten Sided Polygon

decagon

Eleven Sided Polygon

undecagon

Twelve Sided Polygon

dodecagon

diagonal of a polygon

a line segment connecting two nonconsecutive vertices of a polygon

convex polygon

a polygon with no diagonal outside the polygon

Concave Polygon

A polygon that has at least one diagonal with points outside the polygon.

congruent polygons

two polygons whose corresponding sides and angles are congruent

equilateral polygon

a polygon in which all sides are congruent

equiangular polygon

A polygon with all angles have same measure

Regular Polygon

a polygon that is both equilateral and equiangular

Right Triangle

a triangle that has one right angle

acute triangle

A triangle with 3 acute angles

obtuse triangle

a triangle with one obtuse angle

scalene triangle

a triangle with no congruent sides

equilateral triangle

A triangle with three congruent sides

Isosceles Triangle

a triangle with at least two congruent sides

Trapezoid

A quadrilateral with exactly one pair of parallel sides

Kite

a quadrilateral with two distinct pairs of consecutive congruent sides

Parallelogram

A quadrilateral with two pairs of parallel sides

Rhombus

an equilateral parallelogram (all congruent sides, 2 pairs of parallel sides)

Rectangle

an equiangular parallelogram (all congruent angles, 2 pairs of parallel sides)

Square

an equilateral rectangle or an equiangular rhombus or a regular quadrilateral

Circle

The set of all points in a plane that are the same distance from a given point called the center

Radius

The distance from the center of a circle to any point on the edge of a circle

Diameter

A line segment that passes through the center of a circle and has endpoints on the circle

Secant

A line that intersects a circle in two points

chord

A segment whose endpoints lie on a circle

Tangent

A line in the plane of a circle that intersects the circle in exactly one point.

point of tangency

the point where a circle and a tangent intersect

congruent circles

Two or more circles that have the same radius

concentric circles

2 or more coplanar circles with the same center

arc of a circle

two points on the circle and the continuous part of the circle between the two points

semicircle

an arc with endpoints that are the endpoints of a diameter

minor arc

an arc that is less than a semicircle

Major Arc

an arc that is greater than a semicircle

Central Angle

an angle with its vertex at the center of a circle

arc measure

the measure of the corresponding central angle